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<p>Several examples will be given to illustrate some basic concepts of differential equations. First of all, algebraic equations</p>
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\begin{equation}
2 x+1=0 \rightarrow x=-\frac{1}{2}.\tag{1.1.1}
\end{equation}
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<p class="continuation">Then equations involve derivatives <article class="example example-like"><a href="" class="example-knowl original" data-knowl="./knowl/eq1_2-hidden.html" title="Example 1.1.1"><h3 class="heading">
<span class="type">Example</span><span class="space"> </span><span class="codenumber">1.1.1</span><span class="period">.</span>
</h3></a></article> Equations involving derivatives are called <dfn class="terminology">differential equations</dfn>. If the derivatives are only ordinary such as (<a href="" class="xref" data-knowl="./knowl/eq1_2.html" title="Example 1.1.1">Example 1.1.1</a>a), then these equations are called ordinary differential equations (ODEs). If the equations involve partial derivatives such as (<a href="" class="xref" data-knowl="./knowl/eq1_2.html" title="Example 1.1.1">Example 1.1.1</a>b), then they are called partial differential equations (PDEs).</p>
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